EDIT: I'm sorry I didn't read well the question before.
The answer would be No. Your diagram should include the services or functionalities your system provides, so it should include the use case Registration. The internal steps of this process are not included in this kind of diagrams. For that purposes you'll use sequence diagrams for example...
From developer.com:
- Use case: A use case in a use case diagram is a visual representation of a distinct business functionality in a system. The key term here is "distinct business functionality." To choose a business process as a likely candidate for modeling as a use case, you need to ensure that the business process is discrete in nature. As the first step in identifying use cases, you should list the discrete business functions in your problem statement. Each of these business functions can be classified as a potential use case. Remember that identifying use cases is a discovery rather than a creation. As business functionality becomes clearer, the underlying use cases become more easily evident.